2 resultados para Smale’s Conjecture
em Université de Lausanne, Switzerland
Resumo:
Oxytocin (OT) is thought to play an important role in human interpersonal information processing and behavior. By inference, OT should facilitate empathic responding, i.e. the ability to feel for others and to take their perspective. In two independent double-blind, placebo-controlled between-subjects studies, we assessed the effect of intranasally administered OT on affective empathy and perspective taking, whilst also examining potential sex differences (e.g., women being more empathic than men). In study 1, we provided 96 participants (48 men) with an empathy scenario and recorded self reports of empathic reactions to the scenario, while in study 2, a sample of 120 individuals (60 men) performed a computerized implicit perspective taking task. Whilst results from Study 1 showed no influence of OT on affective empathy, we found in Study 2 that OT exerted an effect on perspective taking ability in men. More specifically, men responded faster than women in the placebo group but they responded as slowly as women in the OT group. We conjecture that men in the OT group adopted a social perspective taking strategy, such as did women in both groups, but not men in the placebo group. On the basis of results across both studies, we suggest that self-report measures (such as used in Study 1) might be less sensitive to OT effects than more implicit measures of empathy such as that used in Study 2. If these assumptions are confirmed, one could infer that OT effects on empathic responses are more pronounced in men than women, and that any such effect is best studied using more implicit measures of empathy rather than explicit self-report measures.
Resumo:
The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.